Grass for Shady Area with Runoff

I have a shady side yard about 16 feet wide and 50 feet long with water run off. I had a landscaper recommend dwarf monkey grass. Won't this grass run and take over the yard? I want to stop the water from downspouts, which will be run through a buried pipe, but I am afraid that the monkey grass will take up too much of the yard and get out of control. Any better grasses?

I believe the biggest issue with the Monkey Grass would be the damp ground conditions.
The wet conditions are the biggest issue for you to deal with.

Here are some links that have more information on alternative ground covers and grass that is suitable for shade area.
You may also want to contact your local County Extension Office for a list of turf and plants suitable to your region.